When the two eyes view dissimilar patterns, one experiences a perceptual phenomenon called binocular rivalry. Instead of seeing both patterns superimposed, they are perceived in alternation. What makes this phenomenon remarkable is the dissociation between a constant physical stimulation and fluctuating perceptual experience. Because of this dissociation, binocular rivalry presents an opportunity for studying visual awareness, one of the deepest mysteries facing biomedical science. In spite of widespread interest, and an impressive volume of high-quality work on this topic, many of the central questions concerning the neural processing underlying binocular rivalry remain open. Particularly controversial is the role of primary visual cortex (V1) in rivalry. To address this controversy, we propose to capitalize on an interesting aspect of the perceptual phenomenon; during an alternation, one sees a traveling wave in which the dominance of one pattern emerges locally and expands progressively as it renders the other pattern invisible. Our experiments are designed to measure and characterize the neural basis of these perceptual waves. The proposed experiments will apply a combination of empirical methods (psychophysics and fMRI in humans; optical imaging, electrophysiology, pharmacology, and electrical stimulation in the awake monkey) to explain this perceptual phenomenon in terms of the underlying neural mechanisms and to test the following hypotheses: (1) that competition between the two rival stimuli is implemented by neural circuits in primary visual cortex (V1), i.e., that neural circuits in V1 play a causal role in triggering transitions during rivalry; (2) that for the consequences of this neural competition to be perceived, activity must advance to higher visual areas; and (3) that attention, mediated by feedback from higher visual areas, plays a crucial role in promoting neural activity from V1 to higher visual areas. We will then be in a position to develop and refine a computational theory of the neural processing in V1 that supports these traveling waves, and a theory that elaborates the role of V1 in visual awareness. The neural competition underlying perceptual alternations during rivalry is believed to be closely related to the strabismic suppression. Hence, the proposed experiments will provide useful information and will establish novel experimental protocols that can, in future work; be applied to further our understanding of strabismus and amblyopia.